p-y curves for laterally loaded drilled shafts embedded in weathered rock

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P-y Curves for Laterally Loaded Drilled Shafts

Embedded in Weathered Rock

by

Mohammed A. Gabr, Ph.D., P.E.

Roy H. Borden, Ph.D., P.E.

Kook Hwan Cho

Shane Clark

Joseph B. Nixon

Department of Civil Engineering

North Carolina State University

In Cooperation with

The North Carolina Department of Transportation

and

The institute for Transportation Research and Education

North Carolina State University

Raleigh, North Carolina

December, 2002


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Technical Report Documentation Page

1. Report No.FHWA/NC/2002-008

2. Government Accession No. 3. Recipients Catalog No.

4. Title and SubtitleP-y Curves for Laterally Loaded Drilled Shafts Embedded in Weathered Rock

5. Report DateDecember, 2002

6. Performing Organization Code

7. Author(s)M.A. Gabr, R.H. Borden, K.H. Cho, S.C. Clark, J.B. Nixon

8. Performing Organization Report No.

9. Performing Organization Name and AddressDepartment of Civil Engineering

10. Work Unit No. (TRAIS)

CB 7908 Mann HallNorth Carolina State UniversityRaleigh, NC 27695-7908

11. Contract or Grant No.2002-01

12. Sponsoring Agency Name and AddressNorth Carolina Department of TransportationResearch and Analysis Group1 South Wilmington StreetRaleigh, North Carolina 27601

13. Type of Report and Period CoveredJuly 1999 - June 2002

14. Sponsoring Agency Code2000-01 and 2002-13

15. Supplementary Notes

16. AbstractIn areas of weathered and decomposed rock profiles, the definition of soil parameters needed for the analysis and design of

laterally loaded drilled shafts poses a great challenge. The lack of an acceptable analysis procedure is compounded by theunavailability of a means for evaluating the weathered profile properties, including the lateral subgrade modulus, which often

leads to the conservative design. Results from this research revealed that currently proposed P-y approaches to design drilledshafts embedded in weathered Piedmont profiles do not provide reasonable estimates of load-deflection response. Results in thisreport are used to develop and validate a procedure for the analysis of laterally loaded drilled shafts embedded in a weatheredrock mass. The developed procedure is based on the P-y method of analysis in which the shape and magnitude of the P-y functionare defined. The research proceeded along four complementary tracks: i) Finite Element modeling , ii) Laboratory work, iii) Fieldtesting using full scale shafts; field work also included estimation of in situ modulus of subgrade reaction using rockdilatometer, and finally iv) Performance predictions. The proposed P-y curves are developed as hyperbolic functions. A methodto evaluate in situ stiffness properties of the weathered rock by utilization of the rock dilatometer, as well as by using geologicinformation of joint conditions, RQD, and the strength properties of cored samples, is proposed. A computational scheme forlateral behavior is advanced by which different lateral subgrade responses are assigned in the model based on the location of the

point of rotation. Above the point of rotation, a coefficient of lateral subgrade reaction is assigned on the basis of evaluatedmodulus as computed from rock dilatometer data or from index geologic properties. A stiffer lateral subgrade reaction is assigned

below the point of rotation in order to model the relatively small shear strains in this region. Predictions based on the proposed P-y model for weathered rock show good agreement with field test results, which were performed in various rock profiles. The

proposed method is also verified by comparisons with published results of an additional field test. Concepts of the proposedweathered rock model have been encoded into the computer program LTBASE.

17. Key WordsLaterally Loaded Drilled Shafts, Weathered

Rock, P-y Curves, Rock Dilatometer, SubgradeReaction

18. Distribution Statement

19. Security Classif. (of this report)Unclassified

20. Security Classif. (of this page)Unclassified

21. No. of Pages289

22. Price

Form DOT F 1700.7 (8-72) Reproduction of completed page authorized


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DISCLAIMER

The contents of this report reflect the views of the author(s) and not necessarily the views

of the University. The author(s) are responsible for the facts and the accuracy of the data

presented herein. The contents do not necessarily reflect the official views or policies of

either the North Carolina Department of Transportation or the Federal Highway

Administration at the time of publication. This report does not constitute a standard,

specification, or regulation.


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ABSTRACT

In areas of weathered and decomposed rock profiles, the definition of soilparameters needed for the analysis and design of laterally loaded drilled shafts poses agreat challenge for engineers and contractors. The lack of an acceptable analysis

procedure is compounded by the unavailability of a means for evaluating the weatheredprofile properties, including the lateral subgrade modulus, which often leads to theconservative design.

One of the acceptable approaches to analyze laterally loaded shaft is to model thein situ media as springs, usually characterized in literature as P-y curves. However,results from this research revealed that currently proposed P-y approaches to designdrilled shafts embedded in weathered Piedmont profiles do not provide reasonableestimates of load-deflection response.

Results of the research study presented in this report are used to develop and

validate a procedure for the analysis of laterally loaded drilled shafts embedded in aweathered rock mass. The developed procedure is based on the P-y method of analysis inwhich the shape and magnitude of the P-y function are defined.The research proceededalong four complementary tracks: i) Finite Element modeling using computer programABAQUS for 3-dimensional analysis of resistance forms, ii) Laboratory work to studythe characteristics of P-y curves in simulated material. iii) Field testing using full scaleshafts to develop and verify P-y curves in the weathered rock. Field work also includedestimation of in situ modulus of subgrade reaction using rock dilatometer, and finallyiv) Performance predictions using the developed, and proposed, P-y model to predictmeasured shaft performances, and validate the proposed P-y model.

The proposed P-y curves are developed as hyperbolic functions as this shape isfound to best fit the laboratory and field data. The P-y curves are established as a functionof relative stiffness of the shaft and in situ material. A method to evaluate in situ stiffnessproperties of the weathered rock by utilization of the rock dilatometer, as well as by usinggeologic information of joint conditions, RQD, and the strength properties of coredsamples, is proposed.

A computational scheme of lateral behavior is advanced by which different lateralsubgrade responses are assigned in the model based on the location of the point ofrotation. Above the point of rotation, a coefficient of lateral subgrade reaction is assignedon the basis of evaluated modulus as computed from rock dilatometer data or from index

geologic properties. A stiffer lateral subgrade reaction is assigned below the point ofrotation in order to model the relatively small shear strains in this region and. Predictionsbased on the proposed P-y model for weathered rock show good agreement with field testresults, which are performed in various rock profiles. The proposed method is alsoverified by comparisons with published results of an additional field test. Concepts of theproposed weathered rock model have been encoded into the computer program LTBASE.Details for creating input files using the proposed weathered rock (WR) P-y model arepresented in this report.


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TABLE OF CONTENTS

LIST OF TABLES....................................................................................... ix

LIST OF FIGURES..................................................................................... xi

CHAPTER 1. INTRODUCTION.................................................................1

1.1 Background ............................................................................................................... 11.2 Problem Statement .................................................................................................... 21.3 Objectives ................................................................................................................. 31.4 Scope of Work .......................................................................................................... 4

1.4.1 Finite Element Method Modeling...................................................................... 51.4.2 Laboratory Testing............................................................................................. 51.4.3 Field Testing ...................................................................................................... 6

1.4.3.1 Rock Dilatometer Test ................................................................................ 6

1.4.4 Verification Testing ........................................................................................... 7

CHAPTER 2. LITERATURE REVIEW ...................................................8

2.1 Elastic Approach for Analysis of Laterally Loaded Shafts ...................................... 82.2 P-y Analysis Method............................................................................................... 11

2.2.1 P-y Curve from Measured Strain Data............................................................. 122.3 P-y Curves in Weathered Rock............................................................................... 16

2.3.1 P-y Curves for Weak Rock .............................................................................. 172.3.2 P-y Curve Prediction using Stiff Clay Model .................................................. 20

2.4 Laterally-Loaded, Rock-Socketed, Shafts .............................................................. 212.4.1 Determination of Ultimate Resistance (Pult) of Rock Mass ............................. 232.5 Strength of Jointed Rock Mass ............................................................................... 252.6 Database for North Carolina Rock Properties ........................................................ 27

2.6.1 Site Locations................................................................................................... 272.6.2 Sample Collection............................................................................................ 272.6.3 Sample Identification....................................................................................... 302.6.4 Unconfined Compression Strength.................................................................. 30

2.7 Rock Dilatometer .................................................................................................... 302.7.1 Calculation of Lateral Modulus ....................................................................... 342.7.2 Calculation of the Pressure in Membrane........................................................ 38

2.8 Summary of Literature Review............................................................................... 39

CHAPTER 3. LABORATORY TESTING............................................. 40

3.1 Experimental Program ............................................................................................ 403.1.1 Testing Setup ................................................................................................... 413.1.2 Testing Medium............................................................................................... 41

3.2 F.E.M. Modeling of Laboratory Test...................................................................... 47


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3.3.1 Test Pile Construction...................................................................................... 513.3.2 Test Chamber Filling Procedure and Density Control..................................... 52

3.4 Instrumentation and Data Acquisition .................................................................... 533.4.1 Analysis of Laboratory Strain Data ................................................................. 53

3.5 Laboratory Pile Load Tests..................................................................................... 54

3.5.1 Load Test without Surcharge ........................................................................... 553.5.2 Load Test with Surcharge ................................................................................ 553.6 Measured P-y Curves .............................................................................................. 563.7 Summary of Laboratory Tests ................................................................................ 58

CHAPTER 4. FIELD TESTS................................................................... 59

4.1 Field Load Testing .................................................................................................. 594.1.1 Instrumentation Plan ........................................................................................ 62

4.2 Nash-Halifax County Load Tests............................................................................ 634.2.1 Geology............................................................................................................ 64

4.2.2 Geotechnical Properties of Test Site................................................................ 654.2.3 Description of Test Shafts................................................................................ 664.2.4 Load Test Results............................................................................................. 66

4.2.4.1 Top Deflection and Inclinometer Data ..................................................... 674.2.4.2 Back-calculated P-y Curves...................................................................... 684.2.4.3 Verifying Back-calculated P-y Curves ..................................................... 70

4.3 Caldwell County Load Tests................................................................................... 704.3.1 Geology............................................................................................................ 724.3.2 Geotechnical Properties of Test Site................................................................ 724.3.3 Description of Test Shafts................................................................................ 744.3.4 Load Test Results............................................................................................. 74

4.3.4.1 Top Deflections and Inclinometer Readings............................................. 744.3.4.2 Back-calculated P-y Curves...................................................................... 754.3.4.3 Verifying Back-calculated P-Y Curves from Strain Gages ...................... 78

4.4 Wilson County Load Tests...................................................................................... 784.4.1 Geology............................................................................................................ 794.4.2 Geotechnical Properties of Test Site................................................................ 814.4.3 Description of Drilled Shaft............................................................................. 814.4.4 Load Test Results............................................................................................. 82

4.4.4.1 Top Deflections and Inclinometer Readings............................................. 824.4.4.2 Back-calculated P-y Curves...................................................................... 824.4.4.3 Verifying Back-calculated Results from Strain Gages ............................. 85

4.5 Rock Dilatometer Testing ....................................................................................... 864.6 Summary ................................................................................................................. 88

CHAPTER 5. P-y Model FOR WEATHERED ROCK......................... 90

5.1 P-y Curve Function ................................................................................................. 905.1.1 Curve Fitting of Laboratory Tests Data ........................................................... 92


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5.1.2 Curve Function Based on Field Tests .............................................................. 945.2 Subgrade Modulus (kh) for Weathered Rock.......................................................... 98

5.2.1 Subgrade Modulus (kh).................................................................................... 985.2.2 Modulus from Laboratory Tests ...................................................................... 995.2.3 Subgrade Modulus from Field Tests.............................................................. 100

5.2.4 Comparison of kh0 fromLaboratory and Field Tests...................................... 1015.2.5 Subgrade Modulus from Rock Dilatometer................................................... 1025.2.6 Evaluation of kh with Deformation: Finite Element Study............................ 104

5.2.6.1 Boundary Analysis for Field Modeling .................................................. 1045.2.6.2 Calibration of F.E.M. Modeling ............................................................. 1075.2.6.3 Modeling Field Parameters ..................................................................... 107

5.2.7 Proposed Model for kho in WR Profiles......................................................... 1145.3 Ultimate Resistance (Pult) for Weathered Rock .................................................... 118

5.3.1 Laboratory Test Results ................................................................................. 1195.3.2 Applicability of Pult to Field Results.............................................................. 121

5.4 Validation of Proposed P-y Model ....................................................................... 123

5.4.1 Comparison with Field Data .......................................................................... 1235.4.2 Comparison with Published Load Test (Reese, 1997)................................... 128

CHAPTER 6. VERIFICATION OF P-y MODEL............................... 132

6.1 Test Sites Description ........................................................................................... 1326.1.1 Instrumentation Plan ...................................................................................... 134

6.2 Interstate 40 Load Tests ........................................................................................ 1366.2.1 Geology.......................................................................................................... 1376.2.2 Geotechnical Properties of the Test Site........................................................ 1386.2.3 Description of Drilled Shafts ......................................................................... 140

6.2.4 I-40 Load Test Performance Predictions ....................................................... 1426.2.4.1 I-40 Load Test Predicted-Dilatometer ................................................. 1426.2.4.2 I-40 Load Test Predicted-Geologic Based........................................... 1456.2.4.3 I-40 Load Test Reeses Method and Stiff Clay Model......................... 147

6.2.5 I-40 Load Test Results ................................................................................... 1486.2.5.1 Top Deflections and Inclinometer Readings........................................... 1486.2.5.2 Predicted and Measured Shaft Performance ........................................... 1516.2.5.3 Back Calculated P-y Curves ................................................................... 1516.2.5.4 Predicted and Back Calculated P-y Curves ............................................ 155

6.3 Interstate 85 Load Tests ........................................................................................ 1596.3.1 Geology.......................................................................................................... 159

6.3.2 Geotechnical Properties of the Test Site........................................................ 1616.3.3 Description of Drilled Shafts ......................................................................... 165

6.3.4 I-85 Load Test Performance Predictions ................................................... 1656.3.4.1 I-85 Load Test Performance Predictions ................................................ 166

6.3.5 I-85 Load Test Results ................................................................................... 1706.3.5.1 Top Deflections and Inclinometer Readings........................................... 1706.3.5.2 Predicted and Measured Test Shaft Performance ................................... 1726.3.5.3 Back Calculated P-y Curves ................................................................... 174


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6.3.5.4 Predicted and Back Calculated P-y Curves ............................................ 1766.4 Distribution of the Subgrade Reaction (kh)........................................................... 1806.5 Proposed Design Procedures................................................................................. 181

6.5.1 Design of Laterally Loaded Drilled Shafts using Dilatometer Data.............. 1816.5.2 Design of Laterally Loaded Drilled Shafts using Geologic Data .................. 185

6.6 Inclusion of the Weathered Rock Model in the Computer Program LTBASE(Borden and Gabr, 1987) ............................................................................................ 1906.6.1 Steps for LTBASE Analysis .......................................................................... 190

6.7 Summary of Verification Testing ......................................................................... 191

CHAPTER 7. SUMMARY AND CONCLUSIONS............................. 192

REFERENCES ......................................................................................... 195

BIBLIOGRAPHY..................................................................................... 197

APPENDIX A............................................................................................ 200

APPENDIX B............................................................................................ 205

APPENDIX C............................................................................................ 212

APPENDIX D............................................................................................ 216

APPENDIX E............................................................................................ 223APPENDIX F ............................................................................................ 259

APPENDIX G............................................................................................ 262

APPENDIX H............................................................................................ 265

APPENDIX I ............................................................................................. 267

APPENDIX J............................................................................................. 270


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LIST OF TABLES

Table 1. Material Properties of Rocks .............................................................................. 19

Table 2. Relationships between mb, S, a, and GSI (from Hoek et al., (1995)) ................. 26

Table 3. Value of mi Parameter (Hoek and Brown, 1988) ............................................... 27

Table 4. Rock Mass Rating (RMR) Method (Bieniawski, 1976) ..................................... 28

Table 5. Site and Sample Identification (Parish, 2001) ................................................... 31

Table 6. Unconfined Compressive Strength Database in DTB (Parish, 2001)................. 33

Table 7. Rock Test Data.................................................................................................... 43

Table 8. Modulus of Elasticity of ABC ............................................................................ 46

Table 9. Properties of ABC............................................................................................... 48

Table 10. Properties of Test Piles ..................................................................................... 49

Table 11. Properties of Piles ............................................................................................. 51

Table 12. List of test sites and Rock Types ...................................................................... 60

Table 13. Nash-Halifax County Laboratory Test Results................................................ 66

Table 14. Caldwell County Laboratory Test Results....................................................... 73

Table 15. Wilson County Laboratory Test Results.......................................................... 81

Table 16. Rock Dilatometer Test Sites and Rock Type.................................................... 87

Table 17. Summary of Field Load Tests........................................................................... 89

Table 18. Results of the Lateral Boundary Analysis ...................................................... 106

Table 19. Elements used in F.E.M. Modeling ................................................................ 110Table 20. Properties of Element for Weathered Rock Simulation.................................. 110

Table 21. Properties of Piles ........................................................................................... 110

Table 22. Summary of Points of Rotation versus Flexibility Factor .............................. 116

Table 23. Parameters for Estimation of Pult .................................................................... 120

Table 24. Parameters for Estimation of Pult .................................................................... 122

Table 25. Properties of Test Piles ................................................................................... 128

Table 26. Summary of Statistical Analysis of Sandstone Property ................................ 130

Table 27. RMR Estimation for the Weathered Rock...................................................... 130

Table 28. Verification Test Sites and Rock Types ......................................................... 133

Table 29. I-40 Test Site Core Log .................................................................................. 139

Table 30. I-40 Laboratory Test Results .......................................................................... 139

Table 31. I-40 Rock Dilatometer Results kho Values................................................... 140


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Table 32. Parameters for I-40 Predictions Dilatometer ............................................... 143

Table 33. kh and Pult Values for I-40 Predictions Dilatometer..................................... 145

Table 34. kh Values for I-40 Short Shaft Predictions Geologic Based-Reduced GSI . 146

Table 35. I-85 Test Site Core Log .................................................................................. 162

Table 36. I-85 Laboratory Test Results (Parish, 2001)................................................... 163

Table 37. I-85 Rock Dilatometer Results kho Values................................................... 164

Table 38. Parameters for I-85 Performance Predictions Dilatometer and Geologic Based................................................................................................................................. 166

Table 39. kh and Pult Values for I-85 Load Test Predictions Dilatometer.................... 167

Table 40. kh Values for I-85 Load Test Predictions Geologic Based.......................... 168

Table 41. GSI Values for the Verification Load Tests .................................................. 186

Table 42. LTBASE Input File Format ............................................................................ 190


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LIST OF FIGURES

Figure 1. Some Comparisons of Residual Weathering Profiles (Kulhawy et al., 1991) .... 2

Figure 2. Displacement Influence Factor for Horizontal Load (from Poulos, 1971) ....... 10

Figure 3. Displacement Influence Factor for Moment (from Poulos, 1971) .................... 10Figure 4. Model of a Laterally Loaded Pile (Reese, 1997)............................................... 12

Figure 5. Equilibrium of an Element of Pile..................................................................... 13

Figure 6. Typical Measured Strain from Testing.............................................................. 15

Figure 7. Transition between Residual Soil and Unweathered Rock ............................... 16

Figure 8. Sketch of P-y Curve for Rock (from Reese, 1997) ........................................... 18

Figure 9. Typical P-y Curves Estimated from Reeses Method ....................................... 20

Figure 10. Predicted versus Measured Response (Stiff Clay Model, from Gabr, 1993) .. 21

Figure 11. (a) Shaft and Soil/Rock Mass System; (b) Coordinate System andDisplacement Components; (c) Shear Force V(z) and Moment M(z) Acting on Shaftat depth, z (from Zhang and Einstein, 2000)............................................................. 22

Figure 12. (a) Components of Rock Mass Resistance, (b) Calculation of Normal LimitStress PL (from Zhang and Einstein, 2000)............................................................... 23

Figure 13. Geotechnical Strength Index (Hoek and Brown, 1997) .................................. 25

Figure 14. Test Site Locations within the Durham Triassic Basin (Parish, 2001)............ 29

Figure 15. Component of Rock Dilatometer (Rock Dilatometer Manual, 1999) ............. 35

Figure 16. Typical Pressure/Dilation Graphs for a Pressuremeter Test (Briaud, 1988)... 36

Figure 17. Testing Chamber ............................................................................................. 42

Figure 18. Surcharging and Lateral Loading System ....................................................... 42

Figure 19. Grain Size Analysis of ABC Mixture.............................................................. 44

Figure 20. ABC Triaxial Tests (6 blows for density control)........................................... 45

Figure 21. ABC Triaxial Tests (25 blows for density control)......................................... 46

Figure 22. p-q diagram for ABC Mixture......................................................................... 47

Figure 23. Dimensions and Boundary Conditions for Modeling of Laboratory Test....... 48

Figure 24. Stress Contour of the Laboratory Modeling under Design Load .................... 50

Figure 25. Typical Moment Curvature regression............................................................ 54

Figure 26. Geokon EPC layout ......................................................................................... 55

Figure 27. Stress Distribution ........................................................................................... 56

Figure 28. P-y Curves without Surcharge......................................................................... 57

Figure 29. P-y Curves with Surcharge.............................................................................. 57


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Figure 30. Locations of Test Sites .................................................................................... 60

Figure 31. Layout of Test Shafts with Loading Frame..................................................... 61

Figure 32. Strain Gage and Inclinometer Casing.............................................................. 63

Figure 33. Installation of Steel Cage................................................................................. 63

Figure 34. (a) Loading Frame, (b) Installed Loading Jack and Load Cell........................ 64

Figure 35. Test Area Subsurface Cross-section................................................................ 65

Figure 36. Top Displacements of the Short and Long Shaft Measured from Dial Gages 67

Figure 37. (a) Deflection Profile from Slope Inclinometer Readings -Short Shaft .......... 68

Figure 38. Back-calculated P-y Curves for the Weathered Rock Short Shaft ............... 69


Figure 40. Verifying Back-calculated P-y Curves............................................................ 70

Figure 41. Constructed Test Shaft and Excavated Test Site............................................. 71

Figure 42. Exposed Rock Profile at the Test Site Surface................................................ 71

Figure 43. Load Test Frame and Instrumentation Set-up Profile ..................................... 72



Figure 46. (a) Deflection Profile from Slope Inclinometer Readings - Short Shaft ......... 76


Figure 48. Back-calculated P-y Curves for the Weathered Rock Long Shaft ............... 77

Figure 49. Verifying Back-Calculated P-y Curves ........................................................... 78Figure 50. Exposed Weathered Rock at the Test Site Surface ......................................... 79

Figure 51. Loading Frame and Instrumentation Set-up .................................................... 80



Figure 54. (a) Deflection Profile from Slope Inclinometer Readings -Short Shaft .......... 83


Figure 56. Back-calculated P-y Curves for the Weathered Rock Long Shaft ............... 85

Figure 57. Verifying Back-calculated P-y Curves............................................................ 86

Figure 58. Rock Dilatometer Test Result (Pressure vs. Volume) Caldwell Site A ....... 87

Figure 59. Rock Dilatometer Test Result -Caldwell Site A.............................................. 88

Figure 60. Shape of Assumed P-y Curve (Hyperbolic Curve) ......................................... 91

Figure 61. Transformed Hyperbolic Curve....................................................................... 91

Figure 62. Curve Fitting Laboratory Tests (No Surcharge, Depth = 0.15m) ................... 92


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Figure 95. Initial Moduli of Rock from Pressuremeter (Reese, 1997) ........................... 128

Figure 96. Distribution of Unconfined Compression Strength (c) of Sandstone.......... 129

Figure 97. Top Deflection Comparisons with Data from Reese (1997) ......................... 131

Figure 98. Drilling a Test Shaft I-85 Site .................................................................... 133

Figure 99. Looking from the Hydraulic Jack, East to the Long Shaft I-40 Load Test 134

Figure 100. Instrumented Reinforcement Cage .............................................................. 135

Figure 101. Local Area Map of the I-40 Test Site.......................................................... 136

Figure 102. Exposed Rock at the Elevation of the Test Pad........................................... 137

Figure 103. I-40 Test Site Subsurface Profile................................................................. 138

Figure 104. Rock Dilatometer Test Results I-40 Test Site SB-1................................. 141

Figure 105. Rock Dilatometer Test Results I-40 Test Site SB-2................................. 141

Figure 106. Example of P-y Curve Distribution Used I-40 Short Shaft Shown.......... 144

Figure 107. I-40 Short Shaft Performance Predictions................................................... 147

Figure 108. I-40 Long Shaft Performance Predictions ................................................... 148

Figure 109. Top Deflections of I-40 Short and Long Shafts: Measured from Dial Gages................................................................................................................................. 149

Figure 110. Deflection Profiles after Dial Gage Adjustment I-40 Short Shaft............ 150

Figure 111. Deflection Profiles after Dial Gage Adjustment I-40 Long Shaft............ 150

Figure 112. I-40 Short Shaft Pile Head Deflection Performance ................................... 152

Figure 113. I-40 Long Shaft Pile Head Deflection Performance.................................... 152

Figure 114. Back Calculated P-y Curves for the Weathered Rock I-40 Short Shaft... 153

Figure 115. Back Calculated P-y Curves for the Weathered Rock I-40 Long Shaft ... 153

Figure 116. Curve Fitting Results I-40 Short Shaft ..................................................... 154

Figure 117. Curve Fitting Results I-40 Long Shaft ..................................................... 155

Figure 118. Predicted and Back Calculated P-y Curves I-40 Short Shaft Layer 1...... 156

Figure 119. Predicted and Back Calculated P-y Curves I-40 Short Shaft Layer 3...... 156

Figure 120. Predicted and Back Calculated P-y Curves I-40 Long Shaft Layer 1 ...... 157

Figure 121. Predicted and Back Calculated P-y Curves I-40 Long Shaft Layer 2 ...... 157Figure 122. Predicted and Back Calculated P-y Curves I-40 Long Shaft Layer 3 ...... 158

Figure 123. Predicted and Back Calculated P-y Curves I-40 Long Shaft Layer 4 ...... 158

Figure 124. Local Area Map of the I-85 Test Site.......................................................... 159

Figure 125. Exposed Rock Profile at the Elevation of the Test Pad............................... 160

Figure 126. I-85 Test Site Subsurface Profile................................................................. 160


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CHAPTER 1. INTRODUCTION

1.1 Background

In locations where geologic discontinuities have resulted in relatively soft soils

overlying massive hard rock, the geometry of the soil-rock boundary can be reasonably

defined with existing subsurface exploratory techniques. In areas of weathered and

decomposed rock profiles, such as that of the Piedmont physiographic province of the

southeastern United States, definition of the soil-rock boundary is a recurring challenge

for engineers and contractors. In this situation, the subsurface conditions typically

consist of surface soils derived from extensive weathering of the parent rock. With

depth, the soils grade into less-weathered material and more evidence of the parent rock

features are retained. At some depth, virtually no sign of weathering within the rock

mass can be detected. Quantitative definitions of the soil-rock interface have been

addressed in the literature. Coates (1970) recommended that the Rock Quality

Designation (RQD) value could be used to estimate depth to sound rock. RQD values

less than 25% designate very poor rock quality that could be classified as soil for

engineering purposes. Peck (1976) stated that the distinction between rock-like and soil-

like material in transition zones is usually unpredictable. Figure 1, presented by Kulhawy

et al (1991), showed the depiction of different residual profiles based on definitionsproposed by different researchers.

In these types of transitional subsurface profiles, definition of the soil parameters

needed for the analysis and design of laterally loaded drilled shafts is challenging. The

lack of an acceptable analysis procedure is compounded by the unavailability of a means

for evaluating the weathered profile properties, including the lateral subgrade modulus,

which often leads to overly conservative design of the shaft foundation.

Generally the two most common deformation-based analytical models used in the

analysis of laterally loaded shafts placed in deforming soils and rock are:

1. Subgrade reaction approach (based on the assumption of Winkler foundation).

2. Linear approach based on the theory of elasticity.


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Idealized

Profile

Sowers (1963)

Igneous &

Metamorphic

Deer & Patton (1971)

All Rocks

Demean

(1976)

All Rocks

Engineering

Properties &

Behavior

General

Profile

Top SoilA-Horizons

Soil

B-Horizons

Soil or TrueResidual

SoilResidual

Soil

C-Horizons(Saprolite)

CompletelyWeatheredSaprolite

Saprolite toWeatheredRock

Transition

HighlyWeathered

SoilStructure

Controlled

RelictDiscontinuity

ControlledPartially

WeatheredRock

WeatheredRock

PartlyWeathered

Rock

ModeratelyWeathered

SlightlyWeathered

Solid Rock Unweathered Rock

Fresh Rock

DiscontinuityControlled

Soil

Weathered toUnweatheredRock Mass(Bedrock)

Figure 1. Some Comparisons of Residual Weathering Profiles (Kulhawy et al., 1991)

Numerical models using finite element, finite difference, and boundary element

techniques, with the soil idealized by the subgrade or elastic theory approaches, are often

used as the solution scheme due to the limitations associated with closed-form solutions.

These limitations are mainly related to the difficulty of modeling complicated boundaries,

nonlinearity, inhomogenouity often encountered in geotechnical engineering problems.

1.2 Problem Statement

Past work on the deformation-based analysis of drilled shafts in weathered rock is

scarce. Notable studies recently reported in literature include work by Zhang et al.


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(2000), Reese (1997), and Digioia and Rojas-Gonzalez (1994). Zhang et al. (2000)

considered nonlinear behavior of soil and rock by assuming that the soil and rock mass

are elastic-perfectly plastic materials. Reese (1997) extended the P-y method and utilized

it for the analysis of a single pile in rock. The method was termed interim principally

because of the dearth of load test data to validate the design equations. Digioia and

Rojas-Gonzalez (1994) performed seven tests on drilled shafts supporting transmission

towers and reported the applicability of their design model (MFAD) in predicting the

measured field behavior. They concluded that classical methods for prediction the load-

deflection relationship for drilled shafts in soil consistently over-predict drilled shaft

deflection. They also stated that additional research is necessary to assist the designer

with various rock profiles.

According to the literature reviewed, none of the previous work has been

performed by fully investigating the load-deflection behavior of shafts embedded in

weathered rock. Therefore, it appears that the stiff clay model has been most frequently

used in industry to design shafts embedded in weathered rock, which may be yielding

non-cost effective geometry due to the underestimation of lateral shaft resistance.

Generally, the cost to construct a 1.0 meter diameter drilled shaft is approximately $1,200

per foot. If advanced knowledge can lead to shortening the length of shaft by developing

a P-y curve model for weathered rock, a significant cost saving can be expected.

1.3 Objectives

The general objective of the research program presented in the report is to

develop, validate, and verify a procedure for the design and analysis of laterally loaded

drilled shafts embedded in North Carolina weathered rock profiles. The procedure

developed is based on the P-y method of analysis, in which the shape and magnitude of

the P-y curves will be defined. As previously mentioned, the soil-rock boundary is

largely undefined for the case of a residual soil profile. The current state-of-practice used

by NCDOT for drilled shafts embedded in a weathered Piedmont rock profile is

considered to be over conservative, as it relies on modeling the weathered rock as stiff

clay. Accordingly, cost savings could be realized, while maintaining an acceptable and

safe performance, if a rational method is developed.


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4

From an engineering perspective, the distinction between transitional material and

rock is important in understanding the long-term behavior of a drilled shaft foundation.

Evaluating the lateral stiffness characteristics of the weathered profiles is an essential

analysis component. Such evaluation can be accomplished, in rock profiles, by using in-

situ measuring devices such as the rock dilatometer. However, no in-situ stiffness values

are presently available for discerning the lateral modulus in the Piedmont transitional

profiles.

Specifically, the research program described herein has the following objectives:

1. Enhancement of current understanding of the behavior of drilled shafts embedded

in weathered rock profiles through establishment of performance data from

instrumented field load tests.

2. Development of a P-y model for weathered rock on the basis of laboratory and

field testing, complimented by F.E.M. analysis.

3. Development of a method to estimate the coefficient of subgrade reaction on the

basis of material properties and degree of fixity, as well as in-situ modulus

properties measured using rock dilatometer.

4. Establishment of a database of weathered rock moduli from the North Carolina

Piedmont area using rock dilatometer.

5. Definition of the shape and magnitude of P-y curves and development of a

method to construct these curves for weathered rock using the measured in-situ

properties from the rock dilatometer.

6. Validation of the developed P-y curve model by comparing predicted with

measured load-deformation responses.

7. Verification of the developed P-y curve model utilizing performance predictions

of field tests independent of those used for model development.

1.4 Scope of Work

The scope of work for development of P-y curves in weathered rock proceeded

along four complementary tasks. The first task involved Finite Element modeling using

the ABAQUS computer program for 3-dimensional analysis of resistance media forms.

The second task included laboratory work to study the characteristics of P-y curves in


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simulated material. The third task included field testing using full scale shafts to develop

and validate P-y curves in natural weathered rock materials. And, the final task involved

the application of the developed P-y curve model to field load tests, for which

performance predictions were made prior to testing and then compared with measured

shaft responses. Each of four phases of work is described in the following sections.

1.4.1 Finite Element Method Modeling

Finite Element modeling was performed using the computer program ABAQUS

to design the laboratory testing program and investigate the effects of various field

conditions on the lateral response. Boundary analyses were conducted to discern

boundary effects during laboratory testing based on the diameter and length of the model

pile, the size of testing chamber, and the depth of the soil.

F.E.M. analyses were also used to systematically investigate the effect of relative

stiffness of weathered rock and shaft, and the degree of fixity on the load-deformation

characteristics. In addition, the F.E.M. analyses were utilized for the investigation of

various, possible, field conditions. The comparison and combination of results from

F.E.M. analysis, laboratory testing, and field testing were used to explore situations

beyond those encountered during the laboratory and field experimental programs. Fifty

(50) different scenarios were simulated using F.E.M. by varying analyses parameters

including the magnitude of loading, depth of embedment, and relative stiffness of the

shaft.

1.4.2 Laboratory Testing

Two (2) large scale laboratory tests were performed to evaluate the characteristics

of the P-y curve in simulated material under controlled conditions. The test model shafts

were installed approximately 1 meter into compacted Aggregate Base Course material

(ABC) obtained from Godwin Sand and Gravel in Raleigh, NC. The material wasselected as a weathered rock simulant based on the percentage of recovery from rock

cores obtained in the field from weathered rock profiles. The shape of the P-y curves

were investigated under two different conditions. The first test was performed under self-

weight of simulated material, and the second test under a surcharge of 24 kPa.


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The test results were used to study the phenomena of changing lateral stiffness with depth

and with deformation level. The subgrade modulus and ultimate resistance measured

from laboratory test were compared with those from field test results. The laboratory test

results were used to develop the shape of a mathematical P-y curve function and to

increase the range of relative stiffness within the overall database.

1.4.3 Field Testing

The field load tests were used to develop and verify the P-y curve model for

weathered rock. As a part of the P-y model development, six (6) lateral load tests were

performed in Nash-Halifax County, Caldwell County, and Wilson County in North

Carolina. In addition, four (4) load tests were performed in Durham County as a part of

verification study. All tests were performed on 0.762 meter diameter drilled shafts

instrumented with vibrating wire strain gages. The deflection profile of each shaft was

measured with continuous inclinometer probes. These data were collected to enable the

back-calculation of measured P-y curves with depth. The results of the field test were

used to generate field P-y curves and demonstrate their validity in predicting the

measured load-deformation response of the tested shafts. Results are discussed in view of

measured and predicted responses.

1.4.3.1 Rock Dil atometer Test

Lateral material modulus is needed in order to construct P-y curve for weathered

rock. When the geological conditions were such that the weathered rock is highly

fractured and weathered, it is very difficult to take samples for laboratory test.

Furthermore, when tested in laboratory, the strength and the stiffness properties of the

intact rock fragments were not representative of the in-situ weathered rock mass.

Therefore, if geological conditions vary with depth, in-situ measured properties are

expected to provide the best data for design. An in-situ test method available to measure

rock-mass properties is borehole pressuremeter (referred to as a rock dilatometer modelProbex 1 by ROCTEST, Plattsburgh, NY). The rock dilatometer, manufactured by

ROCTEST is a specialized probe that uses an expandable bladder to apply pressure to the

walls of a N-size borehole. Volume change of the probe is measured at the probe level

under stress increments.


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Nine (9) rock dilatometer tests were performed to provide modulus data for

weathered rock material. A method to construct P-y curve for weathered rock using rock

dilatometer test data, performed at the locations of test shafts, is proposed in this

research.

1.4.4 Verification Testing

Four field load tests are used to verify the applicability of the developed P-y curve

model. Prior to shaft testing, performance predictions were made based on the developed

P-y curve model utilizing strength, stiffness, and geologic parameters measured from

laboratory and field investigations. Performance predictions were also developed using

both of Reeses Methods for P-y curves in weak rock, and Stiff Clay. Results from the

comparison of predicted and measured behavior are discussed. Recommended design

procedures are given based on the results of the verification testing.


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CHAPTER 2. LITERATURE REVIEW

Estimation of load-deflection profiles for laterally loaded shaft has been reported

in literature using several approaches. Poulos (1971) proposed a linear approach based onthe theory of elasticity. Nonlinear load-deflection techniques using the principle of

subgrade reaction is considered most useful for the analysis of laterally loaded piles and

piers.

Reese (1997) proposed a P-y curve method for weathered rock. Zhang et al.

(2000) published a method to estimate the load-resistance profiles for a shaft embedded

in a weathered rock zone. This method assumes that soil and rock have elastic perfectly

plastic characteristics. In either approach, the engineering properties of weathered rock

should be properly determined. The properties of weathered rock can be determined from

either in-situ tests, such as rock dilatometer testing, or using index geological properties

such as unconfined compressive strength, mass joint conditions, and Rock Quality

Designation (RQD). Methods reported in literature for estimating lateral response of

shafts in weathered rock material and lateral modulus properties are discussed in this

chapter.

2.1 Elastic Approach for Analysis of Laterally Loaded Shafts

The theory of elasticity is often used to estimate lateral movement of piles and

shafts in a variety of geomaterial types. One approach, based on the theory of elasticity,

was suggested by Poulos (1971). As presented by Poulos (1971), the lateral behavior of a

given pile was generally influenced by the length-to-diameter ratio, L/d, stiffness of the

pile, and soil strength and stiffness properties The soil in this case was assumed as an

ideal, elastic, homogeneous, isotropic medium, having elastic parameters of Es and s

with depth. The pile was assumed to be a thin rectangular vertical strip of width (d),

Length (L), and constant flexibility (EpIp). In order to apply the analysis to a circular pile,

the width (d) can be taken as the diameter of the pile. To simplify the analysis, horizontal

shear stresses, that develop between the soil and the sides of the pile, were not taken into

account.


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A dimensionless factor KRdescribing the relative stiffness of the pile/soil material

was defined as follows (Poulos, 1971):

4LE

IEK

s

pp

R = (1)

Where, Ep = modulus of elasticity of pile;

Ip = moment of inertia of pile;

Es = modulus of elasticity of soil; and,

L = length of pile.

KR has limiting values of for an infinitely rigid pile and zero for a pile of

infinite length but with no stiffness. The displacement of the pile at the ground surface

was presented using equation 2 and Figures 2 and 3 as follows (Poulos, 1971):

2LE

MI

LE

HI

s

M

s

H += (2)

Where, H = applied horizontal load;

M = applied moment;

IH = the displacement influence factor for horizontal load only, acting on ground

surface (Figure 2); and,

IM = the displacement influence factor for moment only, acting on ground surface

(Figure 3).

The theory of elasticity approach provides a means to estimate the behavior of

drilled shaft based on mathematical derivation. However, in reality, soils and weathered

rock are highly inelastic materials especially under relatively large deformations.

Accordingly, predicted shaft deflections commonly match field deflections at low loads

(20~30% of total capacity). At higher load levels, the predicted deflections are too small

(DiGioia and Rojas-Gonzalez, 1993).


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Figure 2. Displacement Influence Factor for Horizontal Load (from Poulos, 1971)

Figure 3. Displacement Influence Factor for Moment (from Poulos, 1971)

IH

4

s

Pp

RLE

IEK =

IH&

IM

4

s

Pp

RLE

IEK =


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2.2 P-y Analysis Method

Based on the subgrade reaction approach, the soil pressure, p (kN/m2) is

correlated to the lateral deformation as follows (Matlock, 1970):

p = khoy (3)

Where, kho = the coefficient of subgrade reaction that is normally defined on the

basis of Winkler foundation (kN/m3); and,

y = the lateral displacement of the pile (m).

Mltiplying the soil pressure, p (kN/m2), by the pile width, b (m) (or diameter, if

circular), the force per unit length,P(kN/m), is obtained. Accordingly, the soil reaction

P is expressed as the follows:

P =khy (4)

Where

P (kN/m) = soil reaction force per unit length;

kh (kN/m2) = subgrade modulus = kho b;

kho (kN/m3) = coefficient of subgrade reaction; and,

y (m) = pile displacement.

In the subgrade reaction approach for analysis of laterally loaded piles and shafts,

the soil is replaced by a series of springs attached to an element of foundation, as shown

in Figure 4. P-y curves are defined at various depth, as a function of soil type and

geometry.

According to Mattlock (1970), the proper form of a P-y relation is influenced by

many factors, including: (i) natural variation of soil properties with depth, (ii) the general

form of the pile deflection, (iii) the corresponding state of stress and strain throughout the

affected soil zone, and (iv) the rate sequence and history of load cycles. In order to

perform an analysis for a given design, the complex pile-soil interaction is reduced at

each depth to a simple P-y curve.


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P

P

y

y

PlM0

Pv

y

P

P

y

y

P

Figure 4. Model of a Laterally Loaded Pile (Reese, 1997)

2.2.1 P-y Curve from Measured Strain Data

P-y curves from measured data can be evaluated using principles of statics. Two

sets of equations are used to establish the governing differential equation based on

geometry and structural element: the constitutive equation for the pile and the equilibrium

equations for the pile element, as shown in Figure 5. The constitutive equation for the

pile is defined as:

2

2

dz

ydEIEIM == (5)

Where, M = bending moment at depth, z;

E = modulus of elasticity of the pile;

I = moment of inertia of the pile around the centroidal axis of the pile

section;

= pile curvature;

y = pile lateral displacement; and,

z = depth.


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Figure 5. Equilibrium of an Element of Pile

Note that the moment of inertia is taken around the centroidal axis of the pile

cross section. In the case of concrete piles which may crack, the pile cross section is

reduced to account for cracking. In this case it is necessary to first find the neutral axis of

the section, under moments and axial loads, in order to evaluate the part of section that

remains uncracked. Then the centroidal axis of the uncracked section is found and the a

new moment of inertia is calculated around that axis. The horizontal force equilibrium

equation for an element of pile is given as (Figure 5):

dzPdV = (6)

The moment equilibrium equation for the pile element is given as:

dzVdM = (7)

Equations 5, 6, and 7 are combined and lead to the commonly used governing

differential equation (Reese and Welch, 1975):

0Pdz

ydV

dz

ydEI

2

2

4

4

====++++ (8)


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For pile load tests commonly performed in the field, the major data measured are

strains. Stresses acting normal to the cross section of the pile are determined from the

normal strain, x, which is defined as follows:

y

yx == (9)

Where, y = distance to the neutral axis;

= radius of curvature; and,

= curvature of the beam.

Assuming the pile material to be linearly elastic within a given loading range, Hookes

Law for uniaxial stress (=) can be substituted in to equation 9 to obtain equation 10.

yEEy

E xx

=== (10)

Where,x = stress along the x axis; and,

E = Youngs Modulus of the material.

This equation indicates the normal stresses acting along the cross section vary linearly

with the distance (y) from the neutral axis. For a circular cross section, the neutral axis is

located along the centerline of the pile. Given that the moment resultant of the normalstresses is acting over the entire cross section, this resultant can be estimated as follows:

AdyM xo ==== (11)

Noting that Mo is equal to the bending moment, M, and substituting for x from

equation 11, the bending moment can be expressed by equation 12 as:

EI= (12)

Where, = dAyI2

.

This equation can be rearranged as follows:

EI

M==

1(13)


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This equation is known as the moment-curvature equation and demonstrates that

the curvature is directly proportional to the bending moment and inversely proportional to

EI, where EI is the flexural stiffness of the pile.

During a load test, collected strain-evaluated moment data are used to curve fit the

function plotted with depth from the point of load application. Through integration and

differentiation, these data can provide soil reaction values with depth. For example, a

fourth order regression line is selected to curve fit the data shown in Figure 6 and

corresponding variable are obtained as follows:

432 exdxcxbxay ++++= (14)

Where: a, b, c, d, e = the coefficients of the regression line; and,

x = pile segment length (m).

Strain

Location

ofStrainGauge(m)

Figure 6. Typical Measured Strain from Testing

Once this equation is obtained, it is differentiated, with respect to depth, three

times to estimate the resistance of soil P (kN/m). This equation can be integrated twice to

obtain y (m). Alternatively, the lateral deflection can be directly monitored during testing

using inclinometer system. These values are then used to create P-y curves with depth .


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2.3 P-y Curves in Weathered Rock

Residual profiles, such as those found in the piedmont area of the eastern United

States exhibit a transition zone between sound rock and unconsolidated sediments. Over

geologic times, parent rocks are weathered into residual soils, which retain much of the

fabric and many of the structural features of the original rock. The degree of weathering

decreases with depth, usually with no well-defined boundary between soil and rock.

Although the weathering materials have the texture of soils, they retain enough of the

fractures of rock that their behavior under load is often better modeled using methods of

rock mechanics, rather than soil mechanics (Sowers, 1983). The zone between soil and

rock is the focus of this research since many drilled shafts built in Piedmont weathered

rock are placed in, or transgress, this transition zone.

Quantitative definitions of the soil-rock interface have been addressed in the

literature. Deere and Patton (1971) have illustrated idealized residual profile for

metamorphic rock as shown in Figure 7 (a), and intrusive igneous rocks as shown in

Figure 7 (b).

(a) Metamorphic Rock (b) Igneous Rock

Figure 7. Transition between Residual Soil and Unweathered Rock

(from Deer and Patton, 1971)


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Coates (1970) recommended that the Rock Quality Designation (RQD) values be

used to estimate depth to sound rock. RQD values smaller than 25% designated very

poor rock quality that could be classified as soil for engineering purposes. Peck (1976)

stated that the distinction between rock-like and soil-like material in transition zones is

usually unpredictable.

2.3.1 P-y Curves for Weak Rock

Reese (1997), based on two load tests, proposed the only method currently

reported in the literature to construct P-y curves for weak rock. The ultimate resistance

Pur for weak rock was calculated as follows based on limit equilibrium as a function of

depth below ground surface:

Pur= rqurb(1+1.4xr/b), for 0 xr3b (15)

Pur = 5.2rqurb, for xr> 3b (16)

Where, qur= compressive strength of rock, (usually lower-bound as function of depth);

r= strength reduction factor;

b = width, or diameter of pile; and,

xr= depth below rock surface.

If a pile were considered to be a beam resting on an elastic, homogeneous, and

isotropic media, the initial modulus Kir (pi divided by yi) may be shown to have the

following value (Reese, 1997):

Kir= kirEir (17)

Where, Eir= initial modulus of rock; and,

kir= dimensionless constant.

Reese (1997) suggested equation 18 and 19 for kir, which were empirically

derived from experiments and reflected the assumption that the presence of the rock

surface will have a similar effect in kir, as was shown for pur.

kir= (100 + 400xr/3b), for0 xr3b (18)

kir= 500, for xr3b (19)


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Equations 18 and 19 yield the initial portions of the P-y curves and normally provide very

stiff response in order to model the relatively low deflections observed during initial

loading.

With guidelines for computing pur and Kir, equations for the three-parts of P-y

curve are illustrated in Figure 8.

Figure 8. Sketch of P-y Curve for Rock (from Reese, 1997)

Equation 20 defines the straight-line, initial portion of the curves, while the

second and third segments are defined by equations 21 and 22. respectively, Reese

(1997):

P = Kiry, for yyA (20)

25.0

rm

ur )y

y(

2

PP ==== , for yyA and ppur (21)

bky rmrm = (22)

Where, krm = constant, ranging from 0.0005 to 0.00005 and serves to establish

overall stiffness of curves.

The value of yA is found by solving for the intersection of equations 20 and 21,

and is shown by equation 23:

333.1

ir25.0

rm

urA ]

K)y(2

P[y ==== (23)


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Reese (1997) comments on these equations were as follows: First, the equations

have no influence on solutions beyond the value yA (Figure 8) and probably will have no

influence on the designs based on the ultimate bending moment of a pile. Second,

available theory, while incomplete, shows much lower values of Kir in relation to the

modulus of rock or soil. Third, the increase in Kirwith depth in equation 17 is consistent

with results obtained from the lateral loading of piles in overconsolidated clays.

Using equations 20-23, typical P-y curves for Sandstone, Mudstone, and Granite

are constructed and presented in Figure 9. The representative material properties needed

for calculations are based on data summarized in Table 1 (Coon and Merrit, 1970). The

moduli of elasticity for these rock types are decreased by factor of 10 to consider

weathering effects. The diameter of shaft is assumed to 0.762 meter and the depth of

interest is assumed to be greater than 3b (2.3 meters).

Table 1. Material Properties of Rocks

Item Mudstone Sandstone Granite

Elastic Modulus (kN/m2) 7.0107 2.0107 4.0107

Er(Factor of 10) 7.0106 2.0106 4.0106

Compressive Strength (qur)

(kN/m2)10,000 70,000 150,000

Pur(kN/m) 3962.4 27736.8 59436.0


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20

y (mm)

0.00 0.05 0.10 0.15 0.20 0.25

P(kN/m)

0

10000

20000

30000

40000

Mudstone

Sandstone

Granite

Depth > 3b

Figure 9. Typical P-y Curves Estimated from Reeses Method

The P-y curves illustrated in Figure 9 show that the value of Kir is

inconsequential, given its influence at small y. The ultimate resistances for the three

curves are reached a relatively small deflection, in the range of 0.2 mm. It seems for the

data illustrated in Figure 9 that the magnitude of P-y curve is largely dependent on the

strength of the rock. However, in weathered profiles, one can expect that the strength

may depend on the frequency and condition of joints.

2.3.2 P-y Curve Prediction using Stiff Clay Model

Anther possible approach for construction of P-y curves in weathered rock could

be synthesized from that presented by Reese, Cox, and Koop (1975) to model P-y curves

in stiff clay above the groundwater. The shape of the P-y curve for stiff clay was

generated by Reese et al. (1975) using following equation,

4

1

50

)

16

(

y

y

P

P

ur

= (24)

Comparisons of measured and predicted behavior of piers embedded in rock were

performed using equation 24 by Gabr (1993). A stiffer response of P-y curve was

simulated by assuming y50 = 50 B to parametrically study the effect of P-y magnitude on


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the predicted behavior. Predictions were performed using the computer program

LTBASE by Gabr and Borden (1988).

Using y50 = 50 B, compared to y50 = 2.550 B, produced a stiffer P-y response

with shorter initial slope. Consequently, by using y50 = 50 B, the non-linearity effect is

more represented at the early stage of loading as shown in Figure 10. Results showed the

ability to predict the test piers lateral response using P-y model in comparison to the use

of elastic theory.

2.4 Laterally-Loaded, Rock-Socketed, Shafts

Zhang (1999) proposed a method to predict the resistance of laterally loaded rock-

socketed shafts. Figure 11 shows a typical drilled shaft of length L, radius R, and flexural

stiffness EpIp, embedded within a soil and rock profile. The deformation modulus of the

soil was assumed to increase linearly from Es1 at the ground surface to Es2 at the soil and

rock mass interface. The elastic modulus of the rock mass varies linearly from E m1 at the

soil and rock mass interface to Em2 at the shaft tip.

Figure 10. Predicted versus Measured Response (Stiff Clay Model, from Gabr,

1993)


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Zhang et al. proposed a simple method that considered local yielding of the soil

and rock mass and assumed the soil and rock mass to be elastic-perfectly plastic. A

summary of this approach was described as follows (Zhang and Einstein, 2000):

1. Assuming the soil and rock mass are elastic, lateral reaction force (P) is

determined after applying lateral load H and moment M.

2. Compare the computed lateral load reaction force (P) with the ultimate resistance

Pult, and, if P > Pult, determine the yield depth zy in the soil and/or rock mass.

3. Consider the portion of the shaft in the unyielded ground (soil and/or rock mass)

(zy z L) as a new shaft, and analyze it by ignoring the effect of the soil and/or

rock mass above the level z = zy.

4. Repeat Steps (2) and (3). The iteration is continued until no further yielding of the

soil or rock mass occurs.

Figure 11. (a) Shaft and Soil/Rock Mass System; (b) Coordinate System and

Displacement Components; (c) Shear Force V(z) and Moment M(z) Acting on Shaft

at depth, z (from Zhang and Einstein, 2000)


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2.4.1 Determination of Ultimate Resistance (Pult) of Rock Mass

As shown in Figure 12, the total reaction of the rock mass consists of two parts:

the side shear resistance and the front normal resistance. Thus the ultimate resistance Pult

can be estimated as follows (Briaud and Smith, 1983; Carter and Kulhawy, 1992):

Bpp Lult )( max+= (25)

Where, B = diameter of the shaft;

max = maximum shearing resistance along the sides of the shaft; and,

pL = normal limit resistance.

Figure 12. (a) Components of Rock Mass Resistance, (b) Calculation of Normal

Limit Stress PL (from Zhang and Einstein, 2000)

For simplicity, max was assumed to be the same as the maximum side resistance

under axial loading and was given as follows (Zhang, 1999)


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Smooth socket:

5.0

max )(20.0 c = (MPa) (26)

Rough socket:

5.0

max )(80.0 c = (MPa) (27)

Where, c = unconfined compressive strength of the intact rock (MPa).

To determine the normal limit stress PL, the strength criterion for rock masses

developed by Hoek and Brown (1980, 1988) was used. For intact rock, the Hoek-Brown

criterion was expressed in the following form:

5.0

331 1

+

+

=

c

ic m

(28)

Where, c = uniaxial compressive strength of the intact rock material;

1 and 3 = major and minor effective principal stresses, respectively;

mi = material constant for the intact rock.

For jointed rock masses, the Hoek-Brown criterion was given by:

a

c

bc sm

+

+

=

3

31 (29)

Where, mb = value of the constant m for the rock mass; and,

s and a = constants that depend on the characteristics of the rock mass.

Assuming that the minor principal effective stress, 3, was the effective overburden

pressure, z, and the limit normal stress, PL, was the major principal effective stress, 1,

[Figure 12 (b)], the following expression for pL is developed from equation 29 (Hoek

and Brown, 1988):

a

c

bcL smzp

+

+=

=

31 (30)

Where, = effective unit weight of the rock mass; and,


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z = depth from the rock mass surface.

2.5 Strength of Jointed Rock Mass

The strength of a jointed rock mass depends on the properties of the intact rock

pieces and also on the movements of these pieces under different stress conditions, suchas sliding and rotation. This characteristic is controlled by the geometric shape of the

intact rock pieces and the interface condition of the surface between pieces. The

Geotechnical Strength Index (GSI) introduced by Hoek (1994) provides a method to

estimate criteria which are used to calculate rock strength characteristics, as described in

Figure 13.

Figure 13. Geotechnical Strength Index (Hoek and Brown, 1997)


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According to Figure 13, angular rock pieces with clean and rough surface

discontinuities will have greater shearing resistance than a weathered rock mass which

contains rounded pieces surrounded by soil. After the GSI has been determined, the

parameters which described the rock mass strength characteristics can be calculated

based on Hoek et al. (1995) and Hoek and Brown (1997), who proposed the set of

relationships shown in Table 2.

Table 2. Relationships between mb, S, a, and GSI (from Hoek et al., (1995))

Quality of Rock Mass (GSI)

ParameterGood to reasonable (> 25) Good to poor (< 25)

mb imGSI

)28

100exp(

im

GSI)

28

100exp(

S )9

100exp(

GSI 0

A 0.5200

65.0GSI

Table 3 shows values for the parameter mi, which is essentially a function of rock

type (texture and mineralogy) and can be selected according to Hoek and Brown (1988).

The GSI method to define rock mass quality is somewhat imprecise for better

quality rock with GSI > 25. In order to estimate a more precise GSI value for better

quality rock masses, with GSI > 25, it is recommended to use Rock Mass Rating (RMR,

Bieniawski, 1976) method with the ground water rating set to 10 (dry) and the adjustment

for Joint Orientation set to 0, as shown in Table 4 (Hoek and Brown, 1997). However, for

very poor quality rock masses (GSI < 25), the value of RMR is very difficult to estimateand the balance between the different rating systems no longer gives a reliable basis for

estimating rock mass strength (Hoek and Brown, 1997). Therefore, it would be better to

estimate the GSI value from Figure 13.


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Table 3. Value of mi Parameter (Hoek and Brown, 1988)

2.6 Database for North Carolina Rock Properties

A database for engineering characteristics of weathered rock in the Durham

Triassic Basin (DTB) in North Carolina State was presented by Parish (2001).

2.6.1 Site Locations

Twelve locations within the DTB were used to test the engineering properties of

the rock found in the region. Figure 14 shows an area highway map with the locations of

each site identified. Rock cores were retrieved from in-situ materials at all but one

location.

2.6.2 Sample Collection

The collection of samples from DTB area was performed using HX, NX, and BX size

coring. The majority of material recovered was drilled using a 54 mm diameter core or

NX barrel. Larger diameter cores were also used to enable in-situ rock dilatometer


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Table 4. Rock Mass Rating (RMR) Method (Bieniawski, 1976)

Parameter Range of Values

Point LoadStrength

Index

< 8

MPa

> 8

MPa4-8 MPa 1-2 MPa

For this low rangeuniaxial

compressive test ispreferred

Strengthof Intact

RockMaterial Uniaxial

CompressionStrength

< 200MPa

> 200MPa

50-100 MPa 25-50 MPa10-25

MPa

3-10MPa

1-3MPa

1

Rating 15 12 7 4 2 1 0

R.Q.D. 90-100 % 75-90 % 50-75 % 25-50 % 3 m 1-3 m 0.3-1 m 50-300 mm 5 mmthick or Joint open

> 5 mmContinuous joints

4

Rating 25 20 12 6 0

Inflow per 10 m tunnel lengthNone

or< 25 liter/min

or

25-125liters/mi

n

or

25liters/mi

n

or

Ratio

(stressprincipalMajor

pressurewaterJoint)

0or

0.0-0.2or

0.2-0.5or

> 0.5or

GroundWater

General ConditionsCompletely

dry

Moist only(Interstitial

water)

Waterundermod.

pressure

s

5

Rating 10 7 4 0

testing. Cores were taken at varying depths from 1.0 m to 15.5 m. Material from each run

was geologically classified by type, rock quality designation (RQD), and percent

recovery (REC). Samples were retrieved from the twelve different locations within the

DTB identified by NCDOT personnel. Locations where weak materials had previously

been discovered during construction projects were selected for the study. Different rock

types were obtained at varying depths from each site. Thus, within one location, layered


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rock structures occasionally provided alternate types of rock. When the material

properties differed, specimens from each sample depth were catalogued separately and

tested as an independent set of specimens.

Figure 14. Test Site Locations within the Durham Triassic Basin (Parish, 2001)


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2.6.3 Sample Identification

For identification purposes, samples taken from core runs at different locations

within the basin were labeled with a site designation (i.e. Site 1 represented the samples

taken from borings at I-85 and Gregson Street). In addition, depth and type of rock were

also identified. The depth identifier represented the beginning depth at which the

specimen was taken. For rock type, the sandstones were labeled as a and siltstones as

i. Thus a sample identified as 1-3.5i represents a siltstone sample from Site 1 taken at

a depth of 3.5 meter. The site details and sample identifications for materials collected for

this study are listed in Table 5. In general, three specimens for unconfined compressive

strength (qu) testing were obtained for each sample.

2.6.4 Unconfined Compressive Strength

Testing was performed according to ASTM D2938-86, Test Method for

Unconfined Compressive Strength of Intact Rock Core Specimens. Table 6 is a list of the

means and standard deviations of qu for all of the groups of specimens tested in this

study. In general, these means and standard deviations were calculated from the results of

tests on three specimens, as shown in Table 6. In case where less than three specimens

were tested, a subscript is used for identification. In certain instances, for example

specimen 7-4.4i, no standard deviation is listed since only one specimen was tested inthat sample lot. The list also provides depth and sample identifier.

2.7 Rock Dilatometer

One of the most challenging aspects related to the determination of the required

embedment length of drilled shafts in weathered rock is estimating the modulus of lateral

subgrade reaction. A literature review yielded no documentated research that was

performed specifically for characterizing the lateral subgrade modulus of weathered

rocks. In-situ investigation techniques are specially needed in this case since the profilematerials are transitional between soils that can be excavated easily, and massive hard

rock without weakened discontinuities. Since rock in this transition zone is decomposed,

it is challenging to retrieve representative samples. Even when samples are retrieved,

conventional tests, performed on cores, do not provide representative stiffness and

strength characteristics. A relationship between in-situ rock mass modulus and


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laboratory intact modulus values has been presented in the literature by Coon and Merrit

(1970) for higher RQD rocks (typically RQD > 70%). No such relationship exists for the

highly weathered and lower RQD rocks. Unfortunately, the weathering conditions and

the inability to retrieve representative samples from the field necessitate the performance

of in-situ testing if high-quality modulus values are needed.

Table 5. Site and Sample Identification (Parish, 2001)


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Table 5. Site and Sample Id

p-y curves for laterally loaded drilled shafts embedded in weathered rock

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